British Prime Minister David Cameron's decision to allow his cabinet colleagues to campaign their consciences on whether to stay in the European Union may look like inviting chaos. But history suggests it will make his task of winning the referendum easier.

On Tuesday, the prime minister told members of the House of Commons that “it will be open to individual ministers to take a different personal position while remaining part of the government.” That decision breaks with the tradition of "collective responsibility" for government officials, the unwritten rule that cabinet members have to support the government's policies, whether or not they agree with them.

It's tempting to compare Cameron's position to that of Britain's hapless opposition Labour party leader, Jeremy Corbyn, who is so far to the left that much of his cabinet disagree with him on core questions such as whether the U.K. should keep its nuclear deterrent or bomb Syria. Corbyn has been forced to make concessions for fear of splitting the party and is in a constant state of war with senior colleagues. Cameron, however, is no Corbyn.

His move to free ministers to campaign against him in the EU vote was both inspired and in line with the U.K.'s (admittedly short) constitutional history of two previous nationwide referendums -- a 1975 plebiscite on whether to stay in the European Economic Community and a 2011 vote on changing the electoral system. (The Scottish independence referendum was limited to Scotland's 5.3 million residents).

In the 1975 plebiscite, Labour Prime Minister Harold Wilson also surprised policy watchers by allowing his colleagues to campaign for Britain to leave. Wilson won the referendum and retired as a successful and respected leader the following year. After the referendum in 1975, Labour's party unity was restored and Europe became a non-issue until the early 1980s.

In addition to avoiding a damaging split of his party – also one of Wilson’s concerns in 1975 -- Cameron has similarly freed himself to campaign for Britain to stay in Europe, unconstrained by the need to accommodate the views of opponents within his government.

Britain's 2011 referendum on whether to adopt a new electoral system was a condition set by the Liberal Democrats for joining a coalition with Cameron's Conservatives in 2010. The goal was to change Britain's so-called first-past-the-post election system, which tends to squeeze out smaller parties because every vote for a losing candidate is wasted. That referendum failed, but then too ministers were given a free vote, not least because the government was split on party lines; the Liberal Democrats wanted the change and the Conservatives didn't.

Cameron campaigned with gusto against fellow cabinet ministers once the 2011 referendum campaign had started. Freed from the need to present an unconvincing show of unity, the prime minister was able to use the authority of his office to convince the electorate that changes to the status quo would be a leap in the dark. He won by a mile; more than two thirds of voters rejected the proposed new electoral system.

This is also what happened in 1975. Harold Wilson was able to present himself as the standard bearer of stability and to portray his euroskeptic cabinet colleagues Tony Benn and Barbara Castle as fanatics. No longer hampered by the need to show unity where there was none, Wilson convinced a generally skeptical public to vote for Britain to stay in Europe by a 67 percent to 33 percent margin. Cameron will now be free to repeat the success or Wilson.

Like Wilson in the 1970s, Cameron is a pragmatist; he wants Britain to stay in Europe, but feels no missionary zeal for the EU project. And like Wilson, he has cabinet members who see the EU as the root of all evil. These include the Social Security Secretary Iain Duncan Smith and the Leader of the House Chris Grayling, whose resignations over the issue would have been a serious distraction. With the prospect of a referendum as soon as June this year, Cameron had to act fast.

Winning the referendum on EU membership will still not be easy. Both the EU and Britain have changed dramatically since 1975. But if all plays out as it did for Wilson, the decision to suspend collective responsibility for the Brexit referendum could well be the defining decision in Cameron’s premiership, one that saves his political career from the rout that would follow defeat and defines the tactical prime minister as a statesman.

This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.